I try to learn the song as accurately as I can from whatever source. I then sing it a bunch without listening or reading.

My personal opinion, which is right, is that if you change bits of a song just to put your personal scent mark on it, it's evidence of an insecurity that often comes across to people as an ego problem. You don't need to change stuff on purpose. You're not making the song your bitch, you're seducing it. Sing it from the heart, sing it so it feels right, and you can't help but add your own personal touch.

If you like it a certain way, do it that way. Just know that other people may 'own' the song you're singing just as much as you and your changes may be quite unexpected and jarring. People may think you changed something just to leave that scent trail I mentioned earlier, as in, "Hey, I whizzed on that third verse there - it's MINE!" No matter how much you think other people SHOULD accept what you do, if you want them to like what you're doing, think about whether they WILL accept it and like it. It's tough to gauge, and it's the difference between creative genious and arrogant asshole.